scholarly journals Boundedness and persistence of some cyclic-type systems of difference equations

2016 ◽  
Vol 56 ◽  
pp. 78-85 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Difference Equations ◽  
Type Systems ◽  
Cyclic Type ◽  
Boundedness And Persistence

scholarly journals On a solvable class of product-type systems of difference equations

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6113-6129 ◽  
Author(s):  
Stevo Stevic ◽  
Bratislav Iricanin ◽  
Zdenk Smarda
Keyword(s):  
Closed Form ◽  
Difference Equations ◽  
Type Systems ◽  
Product Type ◽  
Dependent Variables ◽  
Solvable Class ◽  
Solvable Product

It is shown that the following class of systems of difference equations zn+1 = ?zanwbn, wn+1 = ?wcnzdn-2, n ? N0, where a,b,c,d ? Z, ?, ?, z-2, z-1, z0,w0 ? C \ {0}, is solvable, continuing our investigation of classification of solvable product-type systems with two dependent variables. We present closed form formulas for solutions to the systems in all the cases. In the main case, when bd ? 0, a detailed investigation of the form of the solutions is presented in terms of the zeros of an associated polynomial whose coefficients depend on some of the parameters of the system.

scholarly journals Global Dynamics of Some Exponential Type Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-24
Author(s):  
A. Q. Khan ◽  
H. M. Arshad ◽  
B. A. Younis ◽  
KH. I. Osman ◽  
Tarek F. Ibrahim ◽  
...  
Keyword(s):  
Fixed Point ◽  
Lyapunov Function ◽  
Exponential Type ◽  
Type Systems ◽  
Global Dynamics ◽  
Dynamical Properties ◽  
Boundedness And Persistence ◽  
Invariant Rectangle ◽  
Theoretical Results ◽  
Positive Fixed Point

We explore the boundedness and persistence, existence of an invariant rectangle, local dynamical properties about the unique positive fixed point, global dynamics by the discrete-time Lyapunov function, and the rate of convergence of some 2,3-type exponential systems of difference equations. Finally, theoretical results are numerically verified.

scholarly journals Investigation of interval stability of linear systems of neutral type of Lyapunov function method

2002 ◽  
Vol 15 (1) ◽  
pp. 71-81 ◽  
Author(s):  
Denis Ya. Khusainov
Keyword(s):  
Difference Equations ◽  
Neutral Type ◽  
Type Systems ◽  
Qualitative Behavior ◽  
Deviating Argument ◽  
Lyapunov Function Method ◽  
Vector Matrix ◽  
The Mathematical Model ◽  
Intensive Development

Systems of differential equations with deviating argument of neutral type [1, 3, 8] are used. The mathematical model takes into account not only the previous moments of time, but also the speed of their change. These equations more adequately describe the dynamics of processes, but their investigation faces significant difficulties. The qualitative behavior of solutions of neutral type systems includes the features both, differential and difference equations [2, 9]. Stability investigations require the smallest size of the delay's speed value [7]. Recently, so-called interval, or robust stability theory has received intensive development. It is based on two theorems of V.L. Kharitonov [4, 5] for scalar: equations. However, difficulties have appeared to obtain similar results for systems in vector-matrix form. It is even more complicated to derive conditions of interval stability for systems of differential-difference equations, though there are results for scalar equation in [6, 10].

scholarly journals Periodic Solution for a Max-Type Fuzzy Difference Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Changyou Wang ◽  
Jiahui Li
Keyword(s):  
Periodic Solution ◽  
Difference Equation ◽  
Difference Equations ◽  
Software Package ◽  
Fuzzy Numbers ◽  
Initial Conditions ◽  
Equation System ◽  
Mathematical Induction ◽  
Inequality Technique ◽  
Boundedness And Persistence

The paper is concerned with the dynamics behavior of positive solutions for the following max-type fuzzy difference equation system: xn+1=maxA/xn, A/xn−1, xn−2, n=0,1,2,…, where xn is a sequence of positive fuzzy numbers, and the parameter A and the initial conditions x−2, x−1, x0 are also positive fuzzy numbers. Firstly, the fuzzy set theory is used to transform the fuzzy difference equation into the corresponding ordinary difference equations with parameters. Then, the expression for the periodic solution of the max-type ordinary difference equations is obtained by the iteration, the inequality technique, and the mathematical induction. Moreover, we can obtain the expression for the periodic solution of the max-type fuzzy difference equation. In addition, the boundedness and persistence of solutions for the fuzzy difference equation is proved. Finally, the results of this paper are simulated and verified by using MATLAB 2016 software package.

scholarly journals Behavior of a Competitive System of Second-Order Difference Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Q. Din ◽  
T. F. Ibrahim ◽  
K. A. Khan
Keyword(s):  
Difference Equations ◽  
Initial Conditions ◽  
Positive Equilibrium ◽  
Positive Real ◽  
Competitive System ◽  
Order Difference ◽  
Rational Difference Equations ◽  
Positive Equilibrium Point ◽  
Boundedness And Persistence ◽  
Theoretical Results

We study the boundedness and persistence, existence, and uniqueness of positive equilibrium, local and global behavior of positive equilibrium point, and rate of convergence of positive solutions of the following system of rational difference equations:xn+1=(α1+β1xn-1)/(a1+b1yn),yn+1=(α2+β2yn-1)/(a2+b2xn), where the parametersαi,βi,ai, andbifori∈{1,2}and initial conditionsx0,x-1,y0, andy-1are positive real numbers. Some numerical examples are given to verify our theoretical results.

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